Find the least common denominator for the following fractions:
3/4, 19/20, 1/6, 3/5, 8/15
Which of these numbers is also divisible by 6 and 15?
20, 40, 60, 80, 100
60
Right. If 60 is also divisible by the other denominators, then it's the least common denominator.
To find the least common denominator (LCD) for a set of fractions, you need to determine the smallest multiple that all the denominators have in common. Here's how you can find the LCD for the given fractions:
Step 1: List the prime factors of each denominator.
- The prime factors of 4 are 2^2.
- The prime factors of 20 are 2^2 * 5.
- The prime factors of 6 are 2 * 3.
- The prime factors of 5 are 5.
- The prime factors of 15 are 3 * 5.
Step 2: Identify the maximum power of each prime factor that appears in the prime factorization of any of the denominators.
- The maximum power of 2 is 2^2.
- The maximum power of 3 is 3.
- The maximum power of 5 is 5.
Step 3: Multiply the maximum powers of the prime factors together.
- 2^2 * 3 * 5 = 60
Therefore, the least common denominator for the fractions 3/4, 19/20, 1/6, 3/5, and 8/15 is 60.